Munster handed the Scots three first-half tries and could not repair the damage, despite having the bulk of possession and territory.
Glasgow had begun the clash in sizzling fashion with a try after just three minutes. Hooker Scott Lawson and flanker Andy Wilson made the first inroads and it was breakaway Stevie Swindall who powered over from the next ruck.
Skipper Dan Parks banged over the tricky conversion – then added two close-range penalties in quick succession to give his side a 14-point cushion.
It took Munster until the 22nd minute to mount their first meaningful attack, but they had to be content with three points from the boot of veteran stand-off Paul Burke for their efforts.
However, the strike just sparked the Warriors into stepping up the pace again and they carved out a clever try straight off the training ground. Winger Rory Lamont deceived his markers by slipping out to the touchline and the crossfield kick by Parks bounced perfectly for him to scoop it up and dive over in the corner.
The Irishmen hit back with a breakout by Test flanker David Wallace, but he lost out in the race to get the vital first touch under the crossbar.
And Glasgow made the most of the let-off by creating a third touchdown, Wilson darting in from close quarters after latching on to a short inside feed from Sam Pinder. Parks converted.
The rattled visitors piled on the pressure in the build up to the break, but the Warriors defence held firm. Tempers wore thin after the restart with referee Nigel Owens handing out a stern warning to Munster substitute Ronan O’Gara and rival centre Andy Craig for a midfield bust-up.
There was more drama five minutes later when Owens awarded the province a penalty try after the home scrummage broke up on their own line. O’Gara slotted the simple conversion.
But Glasgow’s reply was potent as Mike Roberts scampered through to pounce on a grubber chip by Parks, who added the extra points.